Buzza D M A
Polymer IRC, Department of Physics & Astronomy, University of Leeds, LS2 9JT, Leeds, UK.
Eur Phys J E Soft Matter. 2004 Jan;13(1):79-86. doi: 10.1140/epje/e2004-00042-3.
Using the complementary approaches of Flory theory and the overlap function, we study the molecular weight distribution and conformation of hyperbranched polymers formed by the melt polycondensation of A-R(N)(0)-B(f - 1) monomers in their reaction bath close to the mean field gel point p(A) = 1, where p(A) is the fraction of reacted A groups. Here f > or = 3, N(0) is the degree of polymerisation of the linear spacer linking the A group and the f-1 B groups and condensation occurs exclusively between the A and B groups. For Epsilon tripe bond (1-pA) <<1, we assume that the number density of hyperbranched polymers with degree of polymerisation N generally obeys the scaling form n(N) =N(- tau)f(N/Nl) and we explicitly show that this scaling assumption is correct in the mean field regime (here Nl is the largest characteristic degree of polymerisation and the function f (N/Nl) cuts off the power law sharply for N>Nl). We find the upper critical dimension for this system is d(c) = 4, so that for d> or = dc the mean field values for the polydispersity exponent and fractal dimension apply: tau=3/2, d(f) = 4. For d = 3, mean field theory is still correct for Epsilon > Epsilon G where Epsilon G approximately equal N -1 0 is the Ginzburg point; for Epsilon < Epsilon G, mean field theory applies on small mass scales N< N c but breaks down on larger mass scales N> N c where N c approximately equal N 3 0 is a cross-over mass. Within the Ginzburg zone (i.e., d< d(c) < Epsilon G), we show that the hyperbranched chains on mass scales N> N(c) are non-Gaussian with fractal dimension given by d(f) = d (for d = 2,3,4). Our results are qualitatively different from those of the percolation model and indicate that the polycondensation of AB(f-1), unlike polymer gelation, is not described by percolation theory. Instead many of our results are similar to those for a monodisperse melt of randomly branched polymers, a consequence of the fact that tau < 2 so that polydispersity is irrelevant for excluded volume screening in hyperbranched polymer melts.
利用弗洛里理论和重叠函数的互补方法，我们研究了由A-R(N)(0)-B(f - 1)单体在其反应浴中接近平均场凝胶点p(A) = 1处进行熔融缩聚反应形成的超支化聚合物的分子量分布和构象，其中p(A)是反应的A基团的分数。这里f≥3，N(0)是连接A基团和f - 1个B基团的线性间隔基的聚合度，缩聚反应仅发生在A和B基团之间。对于ε三键(1 - pA) <<1，我们假设聚合度为N的超支化聚合物的数密度一般服从标度形式n(N)=N(-τ)f(N/Nl)，并且我们明确表明这种标度假设在平均场区域是正确的（这里Nl是最大的特征聚合度，并且函数f(N/Nl)对于N > Nl时急剧截断幂律）。我们发现该系统的上临界维度为d(c) = 4，因此对于d≥dc，多分散指数和分形维数的平均场值适用：τ = 3/2，d(f) = 4。对于d = 3，当ε > εG时平均场理论仍然正确，其中εG≈N - 10是金兹堡点；对于ε < εG，平均场理论在小质量尺度N < Nc时适用，但在大质量尺度N > Nc时失效，其中Nc≈N30是一个交叉质量。在金兹堡区域内（即，d < d(c) < εG），我们表明质量尺度N > N(c)上的超支化链是非高斯的，其分形维数由d(f) = d给出（对于d = 2,3,4）。我们的结果在定性上与渗流模型的结果不同，并且表明AB(f - 1)的缩聚反应，与聚合物凝胶化不同，不能用渗流理论来描述。相反，我们的许多结果与随机支化聚合物的单分散熔体的结果相似，这是由于τ < 2，以至于多分散性对于超支化聚合物熔体中的排除体积筛选是无关紧要的这一事实的结果。
