Self-Healing Colloidal Crystals

Self-Healing Colloidal Crystals
自愈胶体晶体

The self-assembly of colloidal building blocks is an important tool in the fabrication of photonic materials and sensors, where refractive index periodicity imparts advantageous optical properties. Well-defined colloidal materials have brought benefits to the field of condensed-matter physics, as the large size and slow dynamics of colloidal particles provide an experimentally convenient model system for molecular interactions. Colloidal particles used for these purposes range from hard-sphere materials such as poly(styrene), poly(methylmethacrylate)(PMMA) and silica, as well as hybrid constructs that combine multiple materials to tune the properties of the desired assembly. In this domain, solvent-swollen microgels have been of particular recent interest. These particles interact through much softer interaction potentials than their hardsphere counterparts, thereby dramatically increasing the richness of the resultant phase behavior. Herein, we present a remarkable example of the self-healing properties of microgel colloidal crystals in the presence of particle-size irregularity,which illustrates that such assemblies are intrinsically defect-tolerant because of their ability to dissipate defect energies over long distances through the lattice.
胶体积木的自组装是光子材料和传感器制造中的重要工具，其中折射率周期性赋予有利的光学性质。明确的胶体材料为凝聚态物理领域带来了好处，因为胶体颗粒的大尺寸和慢动力学为分子相互作用提供了实验方便的模型系统。用于这些目的的胶体颗粒包括诸如聚（苯乙烯），聚（甲基丙烯酸甲酯）（PMMA）和二氧化硅的硬球材料，以及组合多种材料以调节所需组件的性质的混合构造。在该领域中，溶剂溶胀的微凝胶是最近特别感兴趣的。这些粒子通过比其硬壳对应物更柔软的相互作用势相互作用，从而显着增加所得相行为的丰富度。在这里，我们提出了一个显着的例子，微粒凝胶晶体在存在粒度不规则的情况下具有自愈特性，这说明这种组件本质上是缺陷耐受的，因为它们能够通过晶格长距离消散缺陷能量。

One of the characteristics of hard-sphere colloidal suspensions with respect to crystal formation is the strict requirement of monodispersed building blocks. Homogenous colloidal crystal nucleation is suppressed in colloidal suspensions with polydispersities greater than10%, and nucleated crystals rarely, if ever, exceed 5.7% polydispersity. These values suggest that the lattice structure contains little or no tolerance for defects or dispersity in lattice constants. However, because of the soft and compressible nature of polymer microgels, it is reasonable to hypothesize that a crystal lattice assembled from microgels may display a certain degree of self-healing within the lattice structure. In this work, we have intentionally introduced large microgel “defects” into microgel assemblies, after which we probed the structure and dynamics in the defect region. We observed that the defect particles are seamlessly integrated into the bulk lattice with no observable perturbation of the lattice structure or dynamics. These observations suggest that self-healing is at play in microgel crystals, where microgel particles can adopt an optimal and uniformly narrow size distribution to accommodate the global energetic demands of the lattice.
关于晶体形成的硬球胶体悬浮液的特征之一是对单分散结构单元的严格要求。在多分散性大于10％的胶体悬浮液中抑制了均匀的胶体晶体成核，并且如果有的话，有核晶体很少超过5.7％的多分散性。这些值表明晶格结构对晶格常数中的缺陷或分散性几乎没有或没有耐受性。然而，由于聚合物微凝胶的柔软和可压缩性质，假设由微凝胶组装的晶格可以在晶格结构内显示出一定程度的自我修复是合理的。在这项工作中，我们有意将大的微凝胶“缺陷”引入微凝胶组件中，之后我们探讨了缺陷区域的结构和动力学。我们观察到缺陷粒子无缝地整合到体晶格中，没有可观察到的晶格结构或动力学的扰动。这些观察结果表明，自愈合在微凝胶晶体中起作用，其中微凝胶颗粒可采用最佳且均匀的窄尺寸分布以适应晶格的全局能量需求。

Figure 1 shows the microgel building blocks under investigation. Figure 1a shows a brightfield transmission optical microscopy image of a crystalline assembly of poly(Nisopropylacrylamide-co-acrylic acid) microgels (pNIPAm– AAc, Rh=(873�66) nm, 3.0 wt% dispersion). These large microparticles are packed to a volume fraction above their canonical freezing point (e.g., >50% fill fraction), thereby driving them into a crystalline assembly. Figure 1b shows a crystalline assembly composed of smaller poly(N-isopropylacrylamide) microgels (pNIPAm, Rh=(357�20) nm, 5.5 wt% dispersion). However, the sample shown in Figure 1b is not composed exclusively of these smaller microgels, but has been doped with a small amount (ca. 0.1 wt%) of the larger pNIPAm–AAc microgels shown in Figure 1a. A dopant particle is present in the center of the image and has been encircled in white.In this image,the dopant is practically indistinguishable from the smaller particles surrounding it, as it has been compressed to accommodate the lattice constant dictated by the major component of the assembly. Experimentally, the only distinguishable feature of the dopant particles is a higher scattering cross-section,which arises from an increased refractive index contrast between the compressed defect particles and the surrounding water molecules. This increase results in brighter particles that produce a scattering halo, which is visible a few lattice planes above the particles and allows for their differentiation relative to the highly solvent swollen “bulk” particles.
图1显示了正在研究的微凝胶构件。图1a显示聚（N-异丙基丙烯酰胺 - 共 - 丙烯酸）微凝胶（pNIPAm-AAc，Rh =（873？66）nm，3.0wt％分散体）的结晶组件的明场透射光学显微镜图像。将这些大的微粒填充至高于其规范凝固点的体积分数（例如，> 50％填充分数），从而将它们驱动成结晶组件。图1b显示了由较小的聚（N-异丙基丙烯酰胺）微凝胶（pNIPAm，Rh =（357-20）nm，5.5wt％分散体）组成的结晶组件。然而，图1b中所示的样品不仅仅由这些较小的微凝胶组成，而是掺杂有少量（约0.1wt％）图1a中所示的较大的pNIPAm-AAc微凝胶。掺杂剂颗粒存在于图像的中心并且已经被白色包围。在该图像中，掺杂剂实际上与其周围的较小颗粒难以区分，因为它已被压缩以适应由组件的主要成分决定的晶格常数。在实验上，掺杂剂颗粒的唯一可区别特征是较高的散射截面，其由压缩的缺陷颗粒与周围的水分子之间的折射率对比度增加而产生。这种增加导致产生散射晕的更亮的颗粒，其在颗粒上方的几个晶格面上可见，并且允许它们相对于高溶剂溶胀的“本体”颗粒进行分化。

The degree to which the assembly exerts control over the swelling behavior of the dopant particles is impressive considering that, in this particular example, the dopant particle occupies a volume that is approximately 15 times smaller than that observed in Figure 1a. In addition to the lack of structural disorder observed, Figure 1c shows the uniformity in diffusion dynamics observedin such assemblies.The particle trajectories observed over approximately 15 seconds (20 frames s�1) are shown as black lines overlaid upon the real-space image. The extents of the “defect” and bulk microgel trajectories are qualitatively indistinguishable from one another. Indeed, the trajectories illustrate that all particles have finite cages in which they diffuse. The particles are not strictly in close contact with their neighbors and are therefore not close-packed, that is, some solvent surrounds each particle to provide as ignificant amount of local mobility. The absence of close-packing, and the translational freedom thus afforded to the particles, is clearly demonstrated when compared witha truly close-packed assembly(Figure 2).Data obtained from a close-packed assembly of pNIPAm–AAc particles (3.5 wt% polymer, pH 3.0, 10 mm ionic strength, effective volume fraction feff�0.74), which has previously been shown to adopt an arrangement in which the particles are truly in contact with one another, are shown in Figure 2a.The close-packed structure is evident by the low diffusivity observed in the trajectories and mean squared displacement (MSD) data. Figure 2b shows a pNIPAm microgel assembly with trajectories and MSD values that indicate a significantly higher diffusivity than that found in the close-packed assembly. However, the pNIPAm crystal is actually a more densely packed assembly than that in Figure 2a, with respect to the degree of particle compression in the lattice (3.8 wt% polymer, feff�0.86). As described below,an effective volume fraction greater than 0.74 indicates that the pNIPAm microgels have been forced to adopt a smaller volume than they attain in dilute solution. In the close-packed pNIPAm–AAc case, the particles are highly restricted in their movement, as seen in the small displacement values and extremely tight trajectories. Conversely, the pNIPAm assembly is much more mobile, as the particles are not mechanically held in a singular lattice site by their neighbors, even though we would naively predict a rigid, tightly packed assembly based on simple volume fraction calculations (see below).
考虑到在该特定实例中掺杂剂颗粒占据的体积比图1a中观察到的体积小约15倍，组件对掺杂剂颗粒的溶胀行为的控制程度令人印象深刻。除了观察到缺乏结构紊乱之外，图1c显示了在这种组件中观察到的扩散动力学的均匀性。在大约15秒（20帧s -1）上观察到的粒子轨迹显示为覆盖在真实空间图像上的黑线。 “缺陷”和体微凝胶轨迹的范围在质量上彼此无法区分。实际上，轨迹表明所有粒子都有有限的笼子，它们在这些笼子中扩散。颗粒并非严格地与它们的邻居紧密接触，因此不是紧密堆积的，即，一些溶剂围绕每个颗粒以提供显着量的局部移动性。与真正紧密堆积的组件（图2）相比，没有紧密堆积和由此提供给颗粒的平移自由度，这清楚地得到证实。数据来自pNIPAm-AAc颗粒的密堆积组件（3.5 wt％）在图2a中示出了聚合物，pH3.0,10mm离子强度，有效体积分数（0.74），其先前已经显示采用其中颗粒彼此真正接触的布置。通过在轨迹中观察到的低扩散率和均方位移（MSD）数据，可以看出密堆积结构。图2b显示了具有轨迹和MSD值的pNIPAm微凝胶组件，其表明比在密堆积组件中发现的显着更高的扩散率。然而，就晶格中的颗粒压缩程度而言，pNIPAm晶体实际上是比图2a中更密集的组件（3.8wt％聚合物，feff≥0.86）。如下所述，有效体积分数大于0.74表明pNIPAm微凝胶被迫采用比在稀溶液中获得的体积更小的体积。在密集的pNIPAm-AAc情况下，粒子的运动受到很大限制，如小位移值和非常紧凑的轨迹所示。相反，pNIPAm组件更具移动性，因为粒子没有被邻居机械地保持在单个晶格位置，即使我们会根据简单的体积分数计算天真地预测刚性，紧密堆积的组件（见下文）。

Considering the results shown in Figure 1, and the odd packing behavior illustrated in Figure 2,the origin of this selfhealing phenomenon is still not immediately obvious. It is clear, however, that the lack of close particle contact argues against a purely mechanical deformation mechanism; that is, the dopant microgel is not simply “squeezed” by its nearest neighbors through particle–particle contacts. Instead, the seamless insertion of the defect into the lattice seems to be facilitated by noncontact forces, such as those that arise from osmotic effects in polymer solutions. The impact of external osmotic pressure on the swelling in polymeric gels has been well studied for both macroscopic gel and microgel particle systems. A number of these investigations have focused on osmotic deswelling of microgels through the addition of linear polymers to the suspension. Saunders and Vincent have observed deswelling in pNIPAm microgel dispersions with poly(ethylene glycol) (PEG) as the polymeric additive, or osmolyte. Upon addition of PEG, the microgels underwent significant deswelling at PEG volume fractions as low as 0.1. Given these results, it may be the case that such effects also dictate the packing energetics in microgel assemblies. However, there are also a number of studies, including our own, that approach neutral microgel interactions solely from the perspective of the colloidal length scale. These studies assume or indirectly measure a short-ranged soft interaction potential between particles, and include no assumptions of long-range interactions such as osmotic deswelling. As discussed below, the data shown in Figures 1 and 2 suggest that the consideration of microgel assemblies in purely colloidal terms is a gross oversimplification; a combination of both colloidal and polymeric energetics conspires to dictate the structure and dynamics of the obtained phases.
考虑到图1所示的结果，以及图2所示的奇数包装行为，这种自愈现象的起源仍然不是很明显。然而，很明显，缺乏紧密的粒子接触反对纯粹的机械变形机制;也就是说，掺杂剂微凝胶不仅仅是通过粒子 - 粒子接触而被其最近邻居“挤压”。相反，缺陷无缝插入晶格似乎是由非接触力促进的，例如那些由聚合物溶液中的渗透作用引起的力。对于宏观凝胶和微凝胶颗粒系统，已经充分研究了外部渗透压对聚合物凝胶中溶胀的影响。许多这些研究集中在通过向悬浮液中添加线性聚合物的微凝胶的渗透消溶胀。 Saunders和Vincent观察到用聚（乙二醇）（PEG）作为聚合物添加剂或渗透剂在pNIPAm微凝胶分散体中消溶胀。加入PEG后，微凝胶在PEG体积分数低至0.1时经历显着的消溶胀。鉴于这些结果，可能的情况是这种效应也决定了微凝胶组件中的填充能量。然而，还有许多研究，包括我们自己的研究，仅从胶体长度尺度的角度来看中性微凝胶相互作用。这些研究假设或间接测量颗粒之间的短距离软相互作用潜力，并且不包括长程相互作用的消极消溶胀的假设。如下所述，图1和图2中显示的数据表明，纯胶体术语中微凝胶组件的考虑是粗略过度简化;胶体和聚合物能量学的组合共同决定了所得相的结构和动力学。

To probe the generality of this phenomenon, we undertook studies of self-healing as a function of microgel concentration (packing density), which can be defined in terms of polymer composition (wt%), but are more applicable to discussions of phase behavior when converted to an effective volume fraction feff. For microgels, the feff value is obtained by fitting dilute solution viscosity data to Batchelor�s equation, thus obtaining a conversion factor that relates the polymer composition (wt%) to a feff value. This method of conversion is necessary because of the lack of a simple polymer-mass to particle-volume relationship in the highly solvent swollen microgels. The conversion factor is calculated from the dilute solution regime where there are virtually no particle–particle interactions. In more concentrated assemblies, a packing maximum is reached; as described above, this maximum is 74% for an face-centered-cubic crystal. To accommodate higher microgel concentrations, the microgels must shrink, as the amount of solvent available is less than that required to reach the swelling limit of the microgels. Indeed, recent neutron scattering experiments clearly illustrate that longrange interactions can contribute to deswelling in microgel suspensions and assemblies. Decreases in the particle radius for a feff value greater than 0.35 (well below the maximum packing fraction of a crystal) and shifts in the peaks of the polymer density profiles were observed, which suggests the deswelling of the particles as a function of concentration.These data suggest that the present method for calculating values of feff is not entirely accurate for 0.35–0.74, and can certainly be expected to diverge quickly from predicted values above 0.74. Accordingly, values of feff above the packing maximum are no longer reasonable representations of the actual volume fraction of the assembly. They are, however, useful for providing a semi-quantitative picture of microgel “overpacking”.
为了探究这种现象的普遍性，我们进行了自我修复作为微凝胶浓度（填充密度）的函数的研究，其可以根据聚合物组成（wt％）来定义，但更适用于相行为的讨论。转换为有效体积分数feff。对于微凝胶，通过将稀溶液粘度数据拟合到Batchelor方程中来获得feff值，从而获得使聚合物组成（wt％）与feff值相关的转换因子。这种转化方法是必要的，因为在高度溶剂溶胀的微凝胶中缺乏简单的聚合物 - 质量与颗粒 - 体积的关系。转化因子由稀溶液方案计算，其中几乎没有颗粒 - 颗粒相互作用。在更集中的组件中，达到最大包装;如上所述，面心立方晶体的最大值为74％。为了适应更高的微凝胶浓度，微凝胶必须收缩，因为可用的溶剂量小于达到微凝胶溶胀极限所需的量。实际上，最近的中子散射实验清楚地表明，长程相互作用可能有助于微凝胶悬浮液和组件中的消溶胀。观察到粒径半径大于0.35（远低于晶体的最大填充率）和聚合物密度分布峰值的变化，这表明粒子的消溶胀是浓度的函数。数据表明，用于计算feff值的本方法对于0.35-0.74并不完全准确，并且当然可以预期从高于0.74的预测值快速偏离。因此，高于填充最大值的feff值不再是组件的实际体积分数的合理表示。然而，它们可用于提供微量凝胶“过度包装”的半定量图像。

Micrographs and particle trajectory maps for crystals with a single central (circled) dopant pNIPAm–AAc microgel over a range of pNIPAm microgel concentrations are shown in Figure 3. The bulk pNIPAm microgels (Rh=(357�20) nm) were synthesized to contain 3 mol% cross-linker and the crystals shown were prepared from various microgel concentrations. In this fashion, the assembly packing densities range from below the hard-sphere limit, to very overpacked assemblies with lattice constants smaller than the dilute solution microgel diameter.Figure 3 shows that as the overall microgel concentration is increased, there is a small but observable decrease in the apparent cage size available to each microgel, as would be expected with denser assemblies. Surprisingly,there is no observable difference in the cage sizes of the dopant particles versus the average bulk particles; the uniformity in structure and dynamics are preserved in the vicinity of the defect with no obvious perturbations. Similar experiments carried out using large pNIPAm particles (Rh= (944�62) nm) as the dopant or defect resulted in qualitatively identical behavior (data not shown). Together, these observations strongly suggest that the dopant particle is experiencing compression because of the osmotic pressure of the highly concentrated microgel environment, and that short-range mechanical deformation is not operative in these assemblies.
在一系列pNIPAm微凝胶浓度下具有单个中心（圆圈）掺杂剂pNIPAm-AAc微凝胶的晶体的显微照片和粒子轨迹图显示在图3中。合成了大量pNIPAm微凝胶（Rh =（357-20）nm）以包含从各种微凝胶浓度制备3mol％交联剂和所示晶体。以这种方式，组装填料密度范围从低于硬球限制，到非常过度包装的组件，晶格常数小于稀溶液微凝胶直径。图3显示，随着整体微凝胶浓度增加，有一个小但可观察到的每个微凝胶可用的表观笼子尺寸减小，如同更密集的组件所预期的那样。令人惊讶的是，掺杂剂颗粒的笼尺寸与平均体积颗粒之间没有可观察到的差异;结构和动力学的均匀性保留在缺陷附近，没有明显的扰动。使用大的pNIPAm颗粒（Rh =（944≤62）nm）作为掺杂剂或缺陷进行的类似实验导致定性相同的行为（数据未显示）。总之，这些观察结果强烈表明掺杂剂颗粒由于高度浓缩的微凝胶环境的渗透压而经历压缩，并且短程机械变形在这些组件中不起作用。

Considering the forces involved in polymer gels, the total osmotic pressure inside a gel consists of mixing pm, elastic pe, and in some cases ionic pi contributions. In good solvents and within the weak screening limit, pm and pi contribute to gel swelling while pe balances these contributions and controls the extent to which the gel is able to swell. At equilibrium,the sum of the contributions must be equal to the external osmotic pressure [Eq. (1)]:
考虑到聚合物凝胶中涉及的力，凝胶内的总渗透压由混合pm，弹性pe和在某些情况下离子π贡献组成。 在良好的溶剂中并且在弱筛选限度内，pm和pi有助于凝胶溶胀，而pe平衡这些贡献并控制凝胶能够溶胀的程度。 在平衡时，贡献的总和必须等于外部渗透压[Eq。（1）]：

The contribution from mixing is heavily dependent upon the Flory polymer–solvent interaction parameter c, and is only varied substantially by changes in temperature or solvent [Eq. (2)]:
混合的贡献在很大程度上取决于Flory聚合物 - 溶剂相互作用参数c，并且仅基本上通过温度或溶剂的变化而变化[等式1]。（2）]：

where NA is the Avogadro constant, kB is the Boltzmann constant, T is temperature, and vs is the molar volume of the solvent. The elastic contribution to swelling is [Eq. (3)]:
其中NA是Avogadro常数，kB是玻尔兹曼常数，T是温度，vs是溶剂的摩尔体积。 对肿胀的弹性贡献是[Eq。（3）]：

where Nc corresponds to the effective number of polymer chains in the gel, kB is the Boltzmann constant, T is temperature, v0 is the volume of the collapsed gel, f0 is the polymer volume fraction within the collapsed gel, and f is the polymer volume fraction in the swollen gel. The elastic contribution is highly dependent on the polymer concentration, or segment density in the gel,which is directly related to the degree of gel swelling. When pext is increased, the sum of the internal pressure contributions must balance the external pressure by deswelling-induced increases in pe.
其中Nc对应于凝胶中聚合物链的有效数目，kB是玻尔兹曼常数，T是温度，v0是塌陷凝胶的体积，f0是塌陷凝胶内的聚合物体积分数，f是聚合物体积 溶胀凝胶中的分数。 弹性贡献高度依赖于聚合物浓度或凝胶中的片段密度，其与凝胶溶胀程度直接相关。 当pext增加时，内部压力贡献的总和必须通过消气诱导的pe增加来平衡外部压力。

In the concentrated microgel solution, pext is primarily controlled by the microgel itself. If we are close to their presence in solution as a pure polymer contribution to pext, then this contribution should equal pm throughout the system. If we assume c = 0.4, we get a pext of about 104Pa. Considering that the experimental values ​​for the bulk modulus of the swollen microgel are in the range of 102-104 Pa, it is reasonable to make the penetration-induced deswelling a considerable factor in the condensation of the dopant particles and the associated self-healing behavior. In addition, due to the presence of longer polymer chains on the surface of the microgel, we may expect that the looser crosslinked microgels should be more interpenetrating. The microgel-microgel interpenetration will reduce the effect of solution osmotic pressure compared to the crosslinked particles used above, as chain interpenetration between microgels increases local segment density and thus increases internal osmotic pressure. . Based on this assumption, 1 mol% of cross-linked pNIPAm microgel (Rh = (395 - 11) nm) was synthesized and assembled with large dopant particles in a range of feff values ​​similar to those shown in Figure 3. The representative data from each concentration is the same as the data shown in Figure 3. There is no difference in local structure and particle mobility near the dopant particles compared to the surrounding particles, although the microfiber crossover is significantly reduced. The density is combined, which increases most of the assembly. This observation also indicates that 1 mol% of the components do not strongly penetrate each other and still apply a sufficiently large osmotic pressure to dissolve the dopant particles, or the polymer concentration and accompanying permeability are still very relevant factors.
This helps the assembly to repair itself. The latter possibility becomes most reasonable when we believe that the polymer concentration contribution does not properly resolve the differences we observe between components. For example, the samples in Figures 1a and 4a each consisted of about 3 wt% polymer, but the pNIPAm-AAc particles apparently experienced two very different external pressures from two different environments. In a homogeneous dispersion (Fig. 1a), the microgels are free to adopt a swollen, space-filling arrangement, whereas when the pNIPAm–AAc microgels are used as dopants in pNIPAm lattices, both the osmolality of the solution and the colloidally imposed lattice constant appear to drive microgel deswelling.
在浓缩的微凝胶溶液中，pext主要由微凝胶本身控制。如果我们接近它们在溶液中的存在作为纯聚合物对pext的贡献，则该贡献应该在整个系统中等于pm。如果我们假设c = 0.4，我们得到约104Pa的pext。考虑到溶胀的微凝胶的体积模量的实验值在102-104Pa的范围内，使渗透诱导的消溶胀成为掺杂剂颗粒和相关自身的冷凝的相当大的因素是合理的。治愈行为。此外，由于微凝胶表面上存在较长的聚合物链，我们可以预期较松散的交联微凝胶应该更具互穿性。与上面使用的交联颗粒相比，微凝胶 - 微凝胶相互渗透将降低溶液渗透压的影响，因为微凝胶之间的链互穿增加了局部区段密度并因此增加了内部渗透压。 。基于该假设，合成1mol％的交联pNIPAm微凝胶（Rh =（395-11）nm）并与大掺杂剂颗粒组装，其具有与图3中所示类似的feff值范围。来自每个浓度的数据与图3中所示的数据相同。尽管微纤维交叉显着减少，但掺杂剂颗粒附近的局部结构和颗粒迁移率与周围颗粒相比没有差异。密度结合在一起，这增加了大部分组件。该观察结果还表明，1mol％的组分不会彼此强烈渗透并且仍然施加足够大的渗透压来溶解掺杂剂颗粒，或者聚合物浓度和伴随的渗透性仍然是非常相关的因素。
这有助于组件自行修复。当我们认为聚合物浓度贡献不能很好地解决我们在组分之间观察到的差异时，后一种可能性变得最合理。例如，图1a和4a中的样品各自由约3wt％的聚合物组成，但pNIPAm-AAc颗粒显然经历了来自两种不同环境的两种非常不同的外部压力。在均匀分散体中（图1a），微凝胶可自由采用溶胀的空间填充排列，而当pNIPAm-AAc微凝胶用作pNIPAm晶格中的掺杂剂时，溶液的重量摩尔渗透压浓度和胶体施加的晶格都是如此。恒定似乎驱动微凝胶消溶胀。

Given these observations it is important to address the colloidal contributions to the osmotic pressure in the microgel assembly. In this case, pext=nkBT, where n is the particle number density. Figure 1 shows 10�10 mm2 images; within the dimensions of these images the homogenous assembly of large microgels contains 40 particles, whereas the doped assembly of small microgels contains 164 particles. Assuming the samples were both assembled at the maximum packing fractions of 0.91 for two-dimensional hexagonally closepacked assemblies and 0.74 for three-dimensional facecentered-cubic crystals, a difference in microgel number densities of an order of magnitude exists between the two samples.For the sample in Figure 1a,n=0.28microgels mm�3, whereas n=2.4 microgels mm�3 for the sample in Figure 1b. Thus, the colloidal osmotic pressures alone are negligible in relation to observed microgel bulk moduli, but the significant difference between them suggests that they could also contribute to the difference in swelling behavior of the pNIPAm–AAc particles between the two samples. The exact manner in which the polymeric and colloidal characteristics of microgel assemblies work together to this end is unclear,but it is not unreasonable to assume, from the observationsmade in this study, that the colloidal number density functions as a form of scaling factor for the polymeric contribution to the external osmotic pressure of the system. Importantly, the observations detailed above make it clear that it is not possible to define microgel behavior by only polymer or colloidal characteristics. Microgel particles are both polymeric and colloidal in nature and the behaviors of assemblies created from these building blocks are subject to both physical characteristics. Whereas it is still unclear how polymer and colloid properties work together to dictate microgel assembly behavior, we have provided one example of how microgel complexity can translate to new and advantageous functionalities such as self-healing.
鉴于这些观察结果，重要的是解决胶体对微凝胶组件中渗透压的贡献。在这种情况下，pext = nkBT，其中n是粒子数密度。图1显示了10？10 mm2的图像;在这些图像的尺寸范围内，大微凝胶的均匀组装包含40个颗粒，而小微凝胶的掺杂组件包含164个颗粒。假设样品的二维六边形封装组件的最大填充率为0.91，三维面心立方晶体的最大填充率为0.74，两个样品之间存在一个数量级的微凝胶密度差异。图1a中的样品，n = 0.28微凝胶mm？3，而对于图1b中的样品，n = 2.4微凝胶mm？3。因此，与观察到的微凝胶体积模量相比，单独的胶体渗透压可忽略不计，但它们之间的显着差异表明它们也可能有助于两种样品之间pNIPAm-AAc颗粒的溶胀行为的差异。微凝胶组件的聚合物和胶体特性为此目的共同工作的确切方式尚不清楚，但从本研究中的观察结果来看，胶体数密度作为聚合物的比例因子的一种形式是不合理的。对系统外部渗透压的贡献。重要的是，上面详述的观察结果清楚地表明，仅通过聚合物或胶体特征来定义微凝胶行为是不可能的。微凝胶颗粒本质上是聚合物和胶体，并且由这些结构单元产生的组件的行为受到两种物理特性的影响。虽然尚不清楚聚合物和胶体特性如何共同决定微凝胶组装行为，但我们提供了微凝胶复杂性如何转化为新的和有利的功能（如自我修复）的一个例子。

Experimental Section

Materials: The monomer N-isopropylacrylamide (NIPAm; Aldrich) was recrystallized from hexane (Fisher Scientific) prior to use. The cross-linker N,N’-methylenebis(acrylamide) (BIS; Aldrich), ammonium persulfate (APS; Aldrich), and acrylic acid (AAc; Fluka) were used as received. All water was purified to 18 MW with a Barnstead E-pure system.
材料：单体N-异丙基丙烯酰胺（NIPAm; Aldrich）在使用前用己烷（Fisher Scientific）重结晶。 交联使用N，N'-亚甲基双（丙烯酰胺）（BIS; Aldrich），过硫酸铵（APS; Aldrich）和丙烯酸（AAc; Fluka）。 用Barnstead E-pure系统将所有水纯化至18MW。

Synthesis: Microgels were synthesized by precipitation polymerization[23] without the addition of surfactant in an aqueous solution (100 mL). The 3 mol% cross-linked pNIPAm microgel synthesis contained NIPAm (1.537 g) and BIS cross-linker (0.065 g), and was initiated with APS (0.037 g). The 1 mol% cross-linked pNIPAm microgel synthesis contained NIPAm (1.569 g) and BIS cross-linker (0.028 g), and was initiated with APS (0.035 g). The 1 mol% crosslinked pNIPAm–AAc microgel synthesis contained NIPAm (1.8 g), BIS cross-linker (0.03 g), and AAc co-monomer (0.2 g), and was initiated with APS (0.05 g). Particles were purified by repeated centrifugation and resuspension.
合成：通过沉淀聚合[23]合成微凝胶，而不在水溶液（100mL）中加入表面活性剂。 3mol％交联的pNIPAm微凝胶合成含有NIPAm（1.537g）和BIS交联剂（0.065g），并用APS（0.037g）引发。 1mol％交联的pNIPAm微凝胶合成含有NIPAm（1.569g）和BIS交联剂（0.028g），并用APS（0.035g）引发。 1mol％交联的pNIPAm-AAc微凝胶合成含有NIPAm（1.8g），BIS交联剂（0.03g）和AAc共聚单体（0.2g），并用APS（0.05g）引发。 通过重复离心和重悬浮来纯化颗粒。

Dynamic light scattering (DLS): The average hydrodynamic radius (Rh) and polydispersity of the particles at 208C were characterized by DLS (Wyatt Technology). Data are an average of 30 measurements with 30 s acquisition times. Samples were equilibrated for 10 min at 208C before measurements were taken. The average Rh of the particles was calculated from the measured diffusion coefficients by using the Stokes–Einstein equation. Diffusion coefficients were determined from the autocorrelation decay functions by using a regularization algorithm included in the manufacturer’s software (Dynamics v6.9.2.9, Wyatt Technology).
动态光散射（DLS）：通过DLS（Wyatt Technology）表征208℃下颗粒的平均流体动力学半径（Rh）和多分散性。 数据是30次测量的平均值，具有30秒的采集时间。 在进行测量之前，将样品在208℃下平衡10分钟。 通过使用斯托克斯 - 爱因斯坦方程从测量的扩散系数计算粒子的平均Rh。 通过使用制造商软件中包括的正则化算法（Dynamics v6.9.2.9，Wyatt Technology）从自相关衰减函数确定扩散系数。

Sample preparation: Homogeneous and doped samples containingvaryingconcentrationsofbulkmicrogels,and(fordopedsamples) 7 mL of a 1 wt% solution of dopant microgels were prepared and introduced into rectangular capillary tubes (VitroCom) that were then sealed to form a closed system as described previously.[42] The inner dimension of these capillaries is 100 mm along the imaging axis, and all microscopic observations were made approximately 50 mm into the sample, thus removing contributions that arise from the glass interface.Samples were allowed to equilibrate for at least 3 days after preparation before any measurements were taken.
样品制备：均匀和掺杂的样品含有不同浓度的块状微凝胶，并且（制备样品）制备7mL 1wt％掺杂剂微凝胶溶液并将其引入矩形毛细管（VitroCom）中，然后将其密封以形成如前所述的封闭系统。] 这些毛细管的内部尺寸沿着成像轴是100mm，并且所有显微镜观察到样品中约50mm，从而消除了由玻璃界面产生的贡献。样品在制备之后至少3天进行平衡，然后进行任何测量。

Microscopy and particle tracking: Particle assemblies were imaged on an Olympus IX71 microscope with a 100� oil immersion objective (1.3 N.A.) in bright field (DIC mode). Images were recorded with Andor Luca EMCCD (Image resolution: 100 mm pixel�1). Samples were maintained at room temperature, approximately208C,duringallexperiments.Imageswererecordedat 20 frames s�1 for 15 s. The obtained image time series were then analyzed on IDL image analysis software (Research Systems, Inc.) with a modified form of particle-tracking routines originally developed by Crocker and Grier.[43] Image analysis established particle position maps from which particle trajectories and MSDs were calculated.
显微镜和粒子追踪：粒子组件在Olympus IX71显微镜上成像，100？ 明场油浸物镜（1.3 N.A.）（DIC模式）。 使用Andor Luca EMCCD（图像分辨率：100mm像素？1）记录图像。 在实验期间将样品保持在室温，约208℃。图像在20帧s -1下记录15秒。 然后在IDL图像分析软件（Research Systems，Inc。）上分析所获得的图像时间序列，其具有最初由Crocker和Grier开发的改进形式的粒子跟踪程序。 图像分析建立了粒子位置图，从中计算出粒子轨迹和MSD。